shikaku

Shikaku, also known as Rectangles, is a logic puzzle that originates from Japan and is published by Nikoli and other puzzle publishers. The puzzle challenges solvers to divide a rectangular grid into a set of non-overlapping axis-aligned rectangles.

In a Shikaku puzzle, some cells contain numbers. Each numbered cell marks exactly one rectangle, and the number in the cell equals the area of that rectangle, measured as the number of grid cells it contains. Each rectangle must be contiguous, include exactly one numbered cell, and the rectangles together must cover every cell of the grid. The numbered cell can lie anywhere inside its rectangle, not necessarily at a corner or edge. A 1 indicates a single-cell rectangle.

Solving typically relies on spatial and arithmetic reasoning. Possible rectangle dimensions are determined by the number (for example, a 6 can be 1x6, 2x3, etc.), and established rectangles place boundaries that constrain neighboring areas. Common techniques include identifying forced placements where a rectangle must extend to fill a row or column, and using the remnants of the grid to rule out impossible shapes. Accurately tracking remaining spaces and the number of cells each unsolved region must contain is essential.

Variants and complexity vary with grid size and clue density. Shikaku puzzles are commonly found in standard rectangular grids ranging from small to large sizes, and can appear with varying numbers of clues. They are popular in puzzle magazines and online platforms, celebrated for their clear rules and reproducible logic.